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Question

A horizontal line is intersected by two parallel lines lower s and lower t that slant from left to right forming eight angles.

If lines s and t are parallel, which pair of angles is supplementary and why?

(1 point)
Responses

∠A
and ∠D
because they are consecutive exterior angles
∠A
and ∠D
because they are consecutive exterior angles

∠A
and ∠B
because they are corresponding angles
∠A
and ∠B
because they are corresponding angles

∠B
and ∠G
because they are consecutive interior angles
∠B
and ∠G
because they are consecutive interior angles

∠G
and ∠D
because they are a linear pair
∠G
and ∠D
because they are a linear pair

Answer 1

To determine which pair of angles is supplementary, let's analyze the angle relationships formed by the two parallel lines (s and t) cut by a transversal (the horizontal line).

In a situation where two parallel lines are intersected by a transversal, supplementary angle pairs can be identified in the following ways:

1. Linear pairs: Two angles that are adjacent and whose non-common sides form a straight line.
2. Consecutive interior angles: Two angles on the same side of the transversal that are interior to the parallel lines.

Given your options, the most appropriate choice is:

∠G and ∠D because they are a linear pair.

This is correct because ∠G and ∠D are adjacent (they share a common vertex and side) and their non-common sides form a straight line, making them supplementary (their measures add up to 180 degrees).